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1. We are given the following labor input requirements:
Cloth
UK
USA
Wheat
2 hours 6 hours
3 hours 2 hours
(a) What is the relative price of cloth in terms of wheat in the UK? In the USA?
In autarky, relative prices are equal to the opportunity cost of production. This is
because, if a positive amount of both goods are demanded, in equilibrium, the
cost of purchasing a good must equal the cost to produce the good. Letting the
USA be home and UK be foreign, we have:
Notice, we wrote in the units for the relative price and opportunity cost.
(b) Where will the free trade price settle post trade? Who will export which good?
If positive amounts of both goods are demanded in each country, then the post
trade price must either be equal to, or rest in between the two autarkic relative
prices. This gives:
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A country will trade whichever good for which they have a comparative advantage.
From the above calculations, since the UK has a lower opportunity cost of cloth in
terms of wheat, they will export cloth and the US will export wheat.
(c) If the post-trade relative price of cloth in terms of wheat is equal to 2/3, show
what happens to consumption of cloth and wheat in the US and UK pre- and posttrade. Use this information to calculate the wage in the USA relative to the UK posttrade.
We answer this question by asking: “How much can we consume with one unit of
labor pre- and post-trade?” Before trade, a country can only consume what it can
produce itself, so it depends on technology (i.e. ULRs). With trade, however, a
country will produce the good for which it has a comparative advantage and can then
either consume it, or trade it at world prices for the other good. We therefore, get the
following:
Table 1: Consumption with 1 Unit of Labor
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Before Trade
After Trade with
Cloth Wheat
Cloth Wheat
UK 1/2 1/6
USA 1/3 1/2
1/2
3/4
1/3
1/2
In the table above, the goods for which a country has a comparative advantage are
underlined in the “Before Trade” columns. We know those amounts are produced
post trade in each of the countries after trade, and then we convert them into the
other good using the relative price of 2/3. This is easily done when we notice the
units on the relative price of cloth in terms of wheat. For example, if the US
produces 1/2 units of wheat, we perform the following calculation to determine how
much cloth they can consume:
1/ 2 wheat × 3 /2 cloth/wheat = 3 /4 cloth
Now, looking at the “After Trade” column, it is easy to verify that the USA is
wealthier because they can consume more of either good with one unit of labor
when compared to the UK. To know by how much, we just have to ask the
question: “What do I have to multiply the UK consumption by in order to get the
equivalent amount in the US?” We find this by the following calculation:
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x = 3/2
Therefore, we can see that the US is 3/2 wealthier than the UK, which implies
w /w∗ = 3/ 2 .
(d) Show that unit labor costs post-trade are consistent with the pattern of trade.
Post-trade, a country should be producing the good for which they have the
lower unit labor cost(ULC). Recall, the ULC for good i is given by ai · w. From the
previous problem we know that w/w∗ = 3/2 . Therefore, if we let w ∗ = 1, then w
= 3/2 . We can then calculate the ULCs for each good in each country.
Table 2: Unit Labor Costs After Trade
Cloth Wheat
UK 2 · 1
USA 3 · 3 /2
Cloth Wheat
6·1 ⇒
3 · 3/2 ⇒
2
6
9/2 3
Indeed, the table confirms the pattern of trade identified in the previous parts of
the problem.
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2. We are given the following labor input requirements for Uruguay and Chile:
Uruguay Chile
Insulation
Grain
Beef
Video Tape
5
15
30
2
2.5
30
30
3
(a) What is the order of products from greatest to least comparative advantage
for Uruguay relative to Chile?
Recall, in the multiple good context, a country has a comparative advantage when
they have a lower ULC. Therefore, for any good i, we want to make the following
comparison:
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The open circles are supposed to represent potential inequalities that we have yet
to fill in. However, notice what we are comparing: the relative wage of Uruguay to
Chile, to the relative ULR of Chile to Uruguay. The higher these relative ULRs,
the more of an advantage Uruguay has at producing that good. We can therefore
list the goods for which Uruguay has the greatest to least comparative advantage
as:
Table 3: Greatest to Least Comparative Advantage for Uruguay.
Grain
2
Video Tape 3/2
Beef
1
Insulation 1 2
(b) Use the numbers provided to draw the relative demand for labor. The y−axis of
the diagram should display the relative wage of Uruguay to Chile (wu/wc).
Figure 1: Relative Demand for Labor
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(c) In equilibrium both Uruguay and Chile produce Video Tapes. What other
products are produced by Uruguay, and what other products are produced by
Chile?
First note that if both Uruguay and Chile produce video tapes, then they must have
the same unit labor cost for producing video tapes. From part (a) we know that
Uruguay has a greater comparative advantage at grain, and so Uruguay must have
higher unit labor costs for producing beef and insulation when compared to Chile.
We therefore have:
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Uruguay: Grain
Chile: Beef and Insulation
(d) What is the relative wage (wu/wc) for Uruguay to Chile when the equilibrium
results in both countries producing Video Tapes?
Again, if both countries produce video tapes, we know both countries must have
the same unit labor costs for producing video tapes. We therefore have:
3. Home (no asterisk) and Foreign (asterisk) produce cheese and wine with the
following unit labor requirements:
Home Foreign
Cheese
Wine
alc = 5 alc∗ = 6
alw = 2 alw∗ = 6
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Home and Foreign have total labor forces of L = 100 and L ∗ = 200 workers.
Before we begin this problem, we should already organize the information we
are given into a single table. This will help us identify all necessary information
with relative ease.
Table 4: Organizing Information
Unit Labor Requirements
Cheese
Wine
Total Feasible Production
Labor Force Cheese
Wine
Home 5
2
100
20 or
50
Foreign 6
6
200
100/3 or 100/3
5/2 2/5
1
1
Notice, we have underlined the good for which each country has a comparative
advantage.
(a) Graph each country’s production possibility frontier and calculate the
opportunity cost of cheese in terms of wine. Which country has an absolute
advantage in cheese produciton, which in wine production? Which country has a
comparative advantage in cheese produciton, which in wine production?
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From the above table, since home has lower unit labor requirements for both goods, it
has an absolute advantage at the production of both goods. However, when
comparing the opportunity cost of cheese in terms of wine, we see that foreign has a
comparative advantage at cheese, and home has a comparative advantage in wine.
Each countries’ production possibility frontier is given below. Note the slope is given
by the opportunity cost of cheese in terms of wine.
Figure 2: Production Possibility Frontiers for Home and Foreign
Home
Foreign
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(b) Using the graph from your precedingg answer, draw each country’s
consumption possibilities in the absence of trade. Calculate the relative prices of
cheese in terms of wine in autarky. We should first recognize that, in the absence
of trade, a country’s consumption possibilities are the same as its production
possibilities. Therefore, the consumption possibilities are given directly by the
PPF. Further, if we assume there is a positive demand for both goods in autarky,
the relative prices will be given by the opportunity cost. The autarkic consumption
possibilities and prices are given below.
Figure 3: Consumption Possibilities for Home and Foreign
Home
Foreign
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(c) Both countries open up to free trade. Graph the relative world supply of
cheese to wine and its response to the relative world price of cheese Pc/Pw base
on the unit labor requirements. Provide specific values on the axes.
We can again refer to the initial table we created in order to draw the relative
supply curve. Knowing that foreign has a comparative advantage at cheese
production, we can use the table to list all specific values. The graph is given
below.
Figure 4: Relative World Supply
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(d) EXTRA CREDIT: World consumer demand for cheese relative to wine depends
on the relative price of the two goods:(Qc + Q∗c )/(Qw + Q∗w) = 6 − 5(Pc/Pw).
Graph the relative demand curve. Calculate the relative price Pc/Pw of cheese in
world trade equilibrium. Calculate the production of Qc , Q∗c , Qw, Q∗w. Calculate
the equilibrium wage rates w and w ∗ under free trade.
To simplify this problem, we will first manipulate relative world demand to a more
user-friendly form. Then we will find the equilibrium and finally graph relative
world demand with relative world supply. Rearranging the demand curve, we get:
Then, plugging in the specialization production ratio of 2/3, we get:
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Notice that the equilibrium price is in between the two autarkic prices, or 16 15 ∈
(1,5/2). Therefore, we know that both countries specialize and the relative demand
curve crosses the relative supply curve on the vertical portion. Graphically we have
the following:
Figure 5: Relative World Supply and Demand
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Given that they both specialize, we know Qc = 0, Q∗c = 100/3, Qw = 50, Q∗w = 0.
Now, to calculate the equilibrium relative wage rates under free trade, we
employ the same technique as in problem 1. We ask ourselves: “what can be
consumed with one-unit of labor under free trade?”
Table 5: Consumption with 1 Unit of Labor
Before Trade
Cheese Wine
Home 1/5
Foreign 1/6
After Trade with
Cheese
Wine
15/32
1/6
½
8/45
1/2
1/6
From the above calculations, we can see that Home is wealthier, and to find out
be how much, we ask ourselves: “what do I have to multiply foreign’s
consumption by to get home’s consumption?”
Therefore, w/w∗ = 45/16.
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